# DOE question….

Six Sigma – iSixSigma Forums Old Forums General DOE question….

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• #48844

annon
Participant

Are strong higher order interactive effects strong indicators of the possible existence of a quadatic relationship?  Can or should the investigator interpret a higher order significance (ie 2way or higher) as requiring a further response surface modeling?
Or would a more efficient approach be to always include centerpoints(s) in the initial characterization and only more toward RSM if curvature is indicated?
Thanks!!

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#165741

Robert Butler
Participant

If you only have two levels for each variable in the design then the presence of a significant interaction is telling you that the relationship between two or more variables is something other than simple addition.
I can’t offer a mathematical proof nor can I point you to any text which might but I can tell you that, in my experience, there hasn’t been any discernable correlation between the existence of interactions and quadratic behavior and I certainly wouldn’t interpret an interaction as implying the existence of curvilinear behavior.
The empirical “proof” for the above comes from the fact that, whenever possible I add a replicated center point to the designs I construct.  I have done this for countless designs in the past 25+ years and the situations of significant effects (curvilinear and interaction, only curvilinear, only interaction, only main effects and curvilinear, only main effects and interactions, etc.) appear to occur at random.
As noted, replication of center points gives a global check for curvilinear behavior. I think it is the most efficient and cost effective way to test for curvilinear behavior and if the curvilinear term does turn out to be significant it provides the justification for further investigation.

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#165825

annon
Participant

Robert, always appreciated.  I will go back and reread my notes…must have missed something…Thanks again!!

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#165853

melvin
Participant

Remember that in setting up the DOE that you are selecting the factors and the levels and that both of those selections impact if the results of your investigation will appear linear or quadratic.
Looking at selecting facors — Suppose you are looking at the incidence of high blood pressure and you select height and weight as your factors.  I’m guessing that neither of those will be nearly as significant as their interaction (low height x high weight).  That situation would not indicate a quadratic function, only that the interaction is what is significant.  I’m also going to guess that center points in this scenario (avg height x avg weight) would confirma a linear relationship.
As to your selection of levels — remember that as you select progressively tighter levels, even the most complicated response will appear linear within that window of observation.  At the other end of the spectrum if you pull back too far even center points may fail to show curvature if you catch the it at the right spot.
But don’t go to RSM until your DOEs have already gotten you to the right factors and levels….
Hope this helped…

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